Yes, I've heard bad things about online backup too, such as slow recovery time - it could take hours or days to recover - and safety concerns, but I'm doing some research and there are some technologies that are much safer, such as PGP for encrypting file stored remotely and SSL for encrypting files during backups and restores.

I am using a Norton online backup and it is good as you are able to save a copy not on a physical hardware you can lose or damage.

What could probably be a major disadvantage is the need to upload all of the files included in your back up, which would be hard if you do not have a stable internet connection on where you are. Though they are able to continue the upload even if you pause them for the meantime, there is no strategic time as you would not know when you would need it.